4.1 The segmentation problem
As a review, segmentation is difficult for the following reasons:

Segmentation is computationally expensive. In order to find valid patterns, a
recognizer must attempt recognition at many different candidate locations.

The segmentation function is complex. To segment successfully, the system
must learn to identify which patterns are valid among the set of all possible
valid and non-valid patterns. This task is intrinsically more difficult than
classification because the space of input is considerably larger. Unlike the space
of valid patterns, the space of non-valid patterns is typically too vast to sample.
This is a problem for many learning algorithms which yield too many false
positives when presented non-valid patterns.

Identifying valid characters among a set of valid and invalid candidates is a
combinatorial problem. For example, correctly identifying which 8 characters
among 20 candidates (assuming 12 false positives), has a 1 in 125,970 (20
choose 8) chances of success by random guessing.

より安全な CAPTCHA が具体的にどういうものかというと、同じ論文内では以下の様に提案されている。

4.2 Building better/harder HIPs
The idea is that the additional arcs are themselves good candidates for false
characters. The previous segmentation attacks would fail on this HIP. Furthermore,
simple change of fonts, distortions, or arc types would require extensive work for
the attacker to adjust to.